Non-Markovianity and coherence of a moving qubit inside a leaky cavity

TL;DR

This study analyzes how a moving qubit inside a leaky cavity experiences non-Markovian dynamics and coherence evolution. By modeling a two-level atom with velocity $v$ interacting with a structured, Lorentzian-type environment, the authors derive a nonlocal evolution for the excited-state amplitude $\tilde{A}(t)$ and connect coherence to $C(t)=|A(t)|$, while quantifying memory effects with the BLP measure $N$. They find that increasing $v$ suppresses the decay rate $\Gamma(t)$ and enhances coherence preservation, but concurrently reduces information backflow, diminishing non-Markovianity; the non-Markovian regime offers stronger coherence protection at a given velocity, though higher cavity quality (smaller $\lambda$) helps sustain memory as velocity grows. The work highlights a controllable trade-off between coherence protection and memory effects, with implications for cavity QED and circuit QED implementations where motion-modulated coupling can be used to optimize quantum resources.

Abstract

Non-Markovian features of a system evolution, stemming from memory effects, may be utilized to transfer, storage, and revive basic quantum properties of the system states. It is well known that an atom qubit undergoes non-Markovian dynamics in high quality cavities. We here consider the qubit-cavity interaction in the case when the qubit is in motion inside a leaky cavity. We show that, owing to the inhibition of the decay rate, the coherence of the traveling qubit remains closer to its initial value as time goes by compared to that of a qubit at rest. We also demonstrate that quantum coherence is preserved more efficiently for larger qubit velocities. This is true independently of the evolution being Markovian or non-Markovian, albeit the latter condition is more effective at a given value of velocity. We however find that the degree of non-Markovianity is eventually weakened as the qubit velocity increases, despite a better coherence maintenance.

Figures (7)

• Figure 1: Schematic illustration of a setup where a single qubit is moving inside a cavity. The qubit is a two-level atom with transition frequency $\omega_0$ traveling with constant velocity v.
• Figure 2: Non-Markovianity as a function of $\beta$ for (a) $\lambda =0.01\gamma$ and (b) $\lambda =0.1\gamma$. Other parameters are taken as: $\alpha =1$, $\Delta =0$, $\omega _{0} =1.53\times 10^{9}$ Hz.
• Figure 3: Non-Markovianity as a function of $\lambda$ for $\beta=0$, $0.05\times10^{-9}$, $0.1\times10^{-9}$. Other parameters are taken as in Fig. 2.
• Figure 4: Coherence $C(t)$ as a function of dimensionless scaled time $\gamma t$ for various velocities of the qubit: (a) $\beta =0$ (solid blue line), $\beta =0.05\times 10^{-9}$ (dotted red line), $\beta =0.1\times 10^{-9}$ (dashed green line); (b) $\beta =0.3\times 10^{-9}$ (solid blue line), $\beta =0.5\times 10^{-9}$ (dotted red line) and $\beta =1.0\times 10^{-9}$ (dashed green line). Values of the other parameters are: $\alpha =\beta =1/\sqrt{2}$, $\lambda =0.01\gamma$, $\Delta =0$, $\omega _{0} =1.53$ GHz.
• Figure 5: The decay rate $\Gamma (t)$ as a function of dimensionless scaled time $\gamma t$ for various velocities of the qubit: (a) $\beta =0$; (b) $\beta =0.05\times 10^{-9}$; (c) $\beta =0.1\times 10^{-9}$; (d) $\beta =1.0\times 10^{-9}$. Other parameters are the same as those used in Fig. \ref{['fig4']}.